Q2. The probability distribution for the number of costumer arrivals per 15-minute period at a restaurant is shown below. x 5 67 8 9101112131415 p(x) (1080.08 0.110.140.18012007 0.05 004003 (a) The probability of 7 costumers arriving per 15-minute period is missing from the table. Calculate this. [1 mark] (b) What is the probability of less than 10 customers to arrive in a 15minute period? [2 marks] (c) Calculate the average number of costumer arrivals per 15- minute period. [2 marks] Q3. A machine that produces stampings for automobile engines is malfunctioning and producing 8% defectives. The defective and non-defective stampings proceed from the machine in a random manner. A sample of the next 15 stampings are selected to be tested. Let X denote the number of defective stampings in the sample. (a) Describe the probability distribution of X including the values of all parameters. [2 marks] (b) Calculate the probability that exactly 2 stampings are found to be defective. [2 marks] (c) If three or more stampings are found to be defective then a larger sample is taken for checking. How often will this happen? (Use the appropriate template). [2 marks] (d) What assumption is required for the validity of the above answers? [1 mark] Q4 Women in the US. have heights that are normally distributed with a mean of 162 cm and standard deviation of 6.6 cm. (a) An airline company have a requirement that a member of the cabin crew must have height between 157 cm and 185 cm. Find the percentage of US. women who satisfy that requirement. r2 men-11:1 Name: Double click here to enter your name 161.101 Statistics for Business ID Number: and ID number ASSIGNMENT 2 DUE WEDNESDAY 11 JANUARY 2023 Total: 40 marks Q1 The following table gives the population distribution of a small villa e, classied b age (in years) at last birthday. AgeIIIIIIaem) m----m One person is selected at random from the village. What is the probability that person is: (a) Female [2 marks] (b) Aged 60 years or over [2 marks] (c) A male between 30 and 59 years old [2 marks] (d) A female given that the person is over 60 years [2 marks] (6) Which two of the above answers would you compare to judge Whether gender and age are independent? What does this comparison suggest? [2 marks] Q2. The probability distribution for the number of costumer arrivals per 15-minute period at a restaurant is shown below. x 5 67 8 9101112131415 p(x) 0.08 0.08 0.1] 0.140.180.1200? 0.05 0.04 0.03 Q4 Women in the U.S. have heights that are normally distributed with a mean of 162 cm and standard deviation of 6.6 cm. (a) An airline company have a requirement that a member of the cabin crew must have height between 157 cm and 185 cm. Find the percentage of U.S. women who satisfy that requirement. [3 marks] (b) What height would only 1 in 100 women exceed? [3 marks] (0) Describe the probability distribution of the average heights from a sample of 20 women from the U.S. What is the probability that in a sample of 20 women the average height will be less than 160 cm? [ 3 marks] Q5 In an experiment with workers from a large factory, the manager collected data on the time required to perform a task. A random sample of 31 workers provided an average of 140 minutes, with a standard deviation of 15 minutes to complete the task. 10 of these workers were over 40 years old. (a) Give a 95% condence interval estimate for the proportion of workers aged 40 years old or over. Write a sentence to interpret this condence interval in context. [3 marks] Condence interval: Interpretation: (b) Give a 95% condence interval estimate for the average time needed for a worker to complete the task. Write a sentence to interpret this condence interval in context. [3 marks] Condence interval: Explanation: (0) Before carrying out the experiment, the manager thought that the average time to complete the task was no more than 130 seconds. Do the results of the experiment suggest that he was wrong? Explain. [2 marks] ((1) Do we need to assume for the analysis in (b) that the time